Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs

Abstract The paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs. The fault and the unknown inputs affect both the state and the output. However, if the dynamical evolution models of the fault and the unknown inputs are available the filtering problem will be solved by the Optimal three-stage Kalman Filter (OThSKF). The OThSKF is obtained after decoupling the covariance matrices of the Augmented state Kalman Filter (ASKF) using a three-stage U–V transformation. Nevertheless, if the fault and the unknown inputs models are not perfectly known the Robust three-stage Kalman Filter (RThSKF) will be applied to give an unbiased minimum-variance estimation. Finally, a numerical example is given in order to illustrate the proposed filters.

[1]  B. Friedland.  Treatment of bias in recursive filtering , 1969 .

[2]  T. R. Rice,et al.  A Two-Stage Filter for State Estimation in the Presence of Dynamical Stochastic Bias , 1992, 1992 American Control Conference.

[3]  José Ragot,et al.  Unbiased minimum-variance filter for state and fault estimation of linear time-varying systems with , 2010 .

[4]  Mohamed Darouach,et al.  Unbiased minimum variance estimation for systems with unknown exogenous inputs , 1997, Autom..

[5]  Peter K. Kitanidis,et al.  Unbiased minimum-variance linear state estimation , 1987, Autom..

[6]  Min-Shin Chen,et al.  Unknown input observer for linear non-minimum phase systems , 2010, J. Frankl. Inst..

[7]  M. Darouach,et al.  Two-stage Kalman estimator with unknown exogenous inputs , 1999, Autom..

[8]  Leang-San Shieh,et al.  Actuator fault detection and performance recovery with Kalman filter-based adaptive observer , 2007, Int. J. Gen. Syst..

[9]  Tao Li,et al.  Fault detection and diagnosis for stochastic systems via output PDFs , 2011, J. Frankl. Inst..

[10]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[11]  Michel Kinnaert,et al.  Diagnosis and Fault-Tolerant Control , 2004, IEEE Transactions on Automatic Control.

[12]  Jian Huang,et al.  Stochastic fault tolerant control of networked control systems , 2009, J. Frankl. Inst..

[13]  Chien-Shu Hsieh,et al.  Optimal solution of the two-stage Kalman estimator , 1999, IEEE Trans. Autom. Control..

[14]  Michael V. Basin,et al.  Optimal filtering over linear observations with unknown parameters , 2009, 2009 American Control Conference.

[15]  Chien-Shu Hsieh,et al.  Robust two-stage Kalman filters for systems with unknown inputs , 2000, IEEE Trans. Autom. Control..

[16]  Chien-Shu Hsieh.  Extension of the robust two-stage Kalman filtering for systems with unknown inputs , 2007, TENCON 2007 - 2007 IEEE Region 10 Conference.

[17]  Chien-Shu Hsieh.  Optimal Minimum-Variance Filtering for Systems with Unknown Inputs , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[18]  R. Patton,et al.  Optimal filtering for systems with unknown inputs , 1998, IEEE Trans. Autom. Control..

[19]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[20]  Chan Gook Park,et al.  The stability analysis of the adaptive two‐stage Kalman filter , 2007 .

[21]  Chan Gook Park,et al.  Adaptive two‐stage Kalman filter in the presence of unknown random bias , 2006 .

[22]  Chien-Shu Hsieh,et al.  Optimal multistage Kalman estimators , 2000, IEEE Trans. Autom. Control..

[23]  R. Patton,et al.  Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances , 1996 .

[24]  Mario Ignagni,et al.  Optimal and suboptimal separate-bias Kalman estimators for a stochastic bias , 2000, IEEE Trans. Autom. Control..

[25]  Mohammed Chadli,et al.  State and unknown input estimation for discrete time multiple model , 2009, J. Frankl. Inst..